FOR THE CRYSTALLIZED ROSEMARY:
10 small rosemary sprigs, no more than 1 inch/3 centimeters each in size (see note)
1 egg white, lightly whisked
2 teaspoons granulated or superfine sugar (caster sugar)
FOR THE CAKE:
About 2 tablespoons/30 grams unsalted butter, softened, for greasing the pan
2 cups/240 grams all-purpose flour (plain flour), more to flour the pan
3/4 cup/160 milliliters extra-virgin olive oil
1/2 cup plus 1 teaspoon/120 grams superfine sugar (caster sugar)
1 tablespoon finely grated orange zest (from about 1 1/2 oranges)
1 1/2 tablespoons/7 grams packed finely chopped rosemary leaves
2 large eggs
1/2 cup/130 grams sour cream
2 teaspoons baking powder
1/4 teaspoon salt
FOR THE ORANGE ICING:
1 1/2 tablespoons freshly squeezed orange juice
2 1/2 teaspoons freshly squeezed lemon juice
1 3/4 cups/175 grams sifted confectioners’ sugar, or 1 1/2 cups/150 grams sifted icing sugar
At least 6 hours before you plan to ice the cake, prepare the crystallized rosemary: Brush rosemary on all sides with a little of the egg white and then dip it in the sugar, so the needles are lightly coated on all sides. Set aside on a wire rack to dry. Repeat with remaining rosemary.
Make the cake: Heat oven to 325 degrees Fahrenheit/160 degrees Celsius. Generously grease a 9-inch/23-centimeter Bundt pan with half the butter and refrigerate for 10 minutes. Butter again, generously, and then flour it, tapping away the excess.
Put olive oil, superfine sugar, orange zest and chopped rosemary leaves in the bowl of an electric mixer fitted with the whisk attachment. Whisk on medium speed until combined, then add eggs, one at a time. Whisk for another minute, until thick, then add sour cream and mix until combined on low speed. Scrape down the sides of the bowl and the whisk.
Sift flour, baking powder and salt together into a small bowl. Add the dry ingredients to the olive oil mixture and mix until combined. Increase speed to high and whisk for 1 minute.
Scrape batter into the Bundt pan and smooth the top with a small spatula. Bake for 30 to 35 minutes, or until cake is cooked and a skewer inserted into the middle comes out clean. Remove from oven and let cool for 10 minutes before inverting onto a serving plate. (You may want to trim the cake at this stage, if it rises unevenly, to allow it to sit flat on the plate.)
Prepare the icing: In a small bowl, whisk together orange juice, lemon juice and confectioners’ sugar until smooth. When the cake has cooled, drizzle icing on top, allowing it to drip down the sides of the cake, then top with the crystallized rosemary and serve.